VosePrincipleRA

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VosePrincipleRA(frequency distribution object, severity distribution object, rho)

This function calculates the insurance premium for given frequency and severity distributions using the Risk Adjusted principle.

Frequency distribution - a frequency distribution object.
Severity distribution - a severity distribution object.
rho - see the formula below.

For an insurance policy the premium charged must be at least greater than the expected payout E[X]. Otherwise, according to the law of large numbers, in the long run the insurer will be ruined. The question is then: how much more should the premium be over the expected value?

The Risk Adjusted principle is a special case of the Proportional Hazards Premium Principle based on coherent risk measures (see, e.g. Wang (1996). The survival function (1-F(x)) of the aggregate distribution which lies on [0,1] is transformed into another variable that also lies on [0,1]

Premium = r > 1

where F(x) is the cumulative distribution function from the aggregate distribution.